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by: Michale Kuhlman

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# Intro CalcBusiness Applicatio MATH 108

Marketplace > George Mason University > Mathematics (M) > MATH 108 > Intro CalcBusiness Applicatio
Michale Kuhlman
Mason
GPA 3.85

Staff

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COURSE
PROF.
Staff
TYPE
Study Guide
PAGES
2
WORDS
KARMA
50 ?

## Popular in Mathematics (M)

This 2 page Study Guide was uploaded by Michale Kuhlman on Monday September 28, 2015. The Study Guide belongs to MATH 108 at George Mason University taught by Staff in Fall. Since its upload, it has received 51 views. For similar materials see /class/215008/math-108-george-mason-university in Mathematics (M) at George Mason University.

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Date Created: 09/28/15
Math 108 Final Exam Topics Spring 2008 The best way to study for the nal is to rework your old tests and quizzes and to work the problems in the chapter reviews Here are some other problems to help you focus We will begin the review on Monday with questions on these I will post answers after Monday s review session N E 4 UI Domain of a function Identify the domain of each of the functions 12x 3x6 gxm and fx 9 x fx gxxquot 6x35x 3 fxxrlnx gxe x x2 5x 439 limits exist fx LEI95 lxigfoc and fx Limits Consider the function f x Find the following limits if the Continuity Is the function f 6 continuous atx 2 Is it continuous x3 if x S 2 atx3 4x lz39fxgt2 Why or why not f x State the general definition of the derivative of a function using limits Find f x using the limit de nition where f x 2x2 3x Derivatives power rule constant rule constant multiple rule product rule quotient rule chain rule log and exponential rules Find f x for the following functions 21 fx 4x5 12x4 3xx4 7L393 w fx 4 C 9x3 2x d 1JC3X2 75 5 52 fx ln4x2 1 f f x x2 3x 9ln 3x D V fx x3 esxlnx 73 fx auxin V g h V gt1 9 0 O N LA Implicit differentiation nd y39 if xy x4 4 y3 Second derivatives nd f if fx 6x3 2x4 if fx 5000x264 Z or if fx x2 rlnxz Equations of tangent lines find an equation of the line tangent to fx at the given value of x a fx 2x3 12 at x l b fx e2 2 at x1 c fxxgtlnx4 at xl Intervals of increase relative maXima and minima Find the critical values of each of the functions find the intervals of increase and decrease and classify the critical values as relative maXima minima or neither where f x 3x4 8x3 16 3x 5 37 2 gx 271 fx e 3 gx ln2x 1 For all ofthe above functions also x find the second derivative find the in ection points and use the second derivative test to con rm your results Evaluate a nix5f b log1312252 0 82103834410382 Use the properties of exponents and logarithms to simplify if possible 3 x a 1n 7 b log3 x6 27 x4 x6 0 x3y25 Solve for x a 102 43x b ln4x l ln3 ln5 c log3 4x 1 3 d In 4 lnx l lnx 2 Marginal cost marginal revenue A manufacturer of widgets estimates that his total cost of producing q units is Cq q2 q 20 and that he can sell all q units ifthe price per unit is pq 23 61 Find the marginal cost Find the revenue function Rq and nd the marginal revenue Use the marginal cost to estimate the cost of producing the fth unit Find the pro t function Hint Pro t total revenue 7 total cost Find the marginal profit At what level of production is pro t maximized

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